1D Euler Equations

The 1D Euler equations represent instationary, inviscid, compressible flows in a single space dimension, typically to model states in a tube. It is configured by setting the name in the equation table to euler_1d.

Here is an example for the equation table of this equation system:

  equation = {
    name      = 'euler_1d',
    isen_coef = 1.4,
    r         = 287,
    numflux   = 'hll',
    material = {
      characteristic = 0.0,
      relax_velocity = 0.0,
      relax_temperature = 0.0
    }
  }
  equation.cv = equation.r / (equation.isen_coef - 1.0)

The fluid is described by the ideal gas constant (equation.r), the isentropic expansion coefficient (equation.isen_coef) and the isochoric specific heat (equation.cv). See atl_eqn_euler_module for all options.

Note: you have to use the modg_1d scheme to compute this equation system (scheme.spatial.name = 'modg_1d').

The following example setups are available:

• Modal Estimate: illustrates the use of a modal estimation for the adaptive time step computation based on the CFL condition.

• Shock Stabilization: demonstrates the use of a spectral and covolume filter to stabilize the simulation for a single moving shock.

• Toro: utilizes a Riemann problem setting and simulates a shock tube.

• Piston: shock formation due to the sudden movement of a piston geometry.

• modereduction: shock formation due to the sudden movement of a piston geometry. Reduced computation of the physical fluxes inside the piston through the mode reduction feature.